If LPG cylinder contains mixture of butane and isobutane, then the amount of oxygen that would be required for combustion of 1 kg of it will be

Options

A. `1*8 kg`
B. `2*7 kg`
C. `4*5 kg`
D. `3*58 kg`

Explanation

To determine the amount of oxygen required for the combustion of 1 kg of a mixture of butane (C4H10) and isobutane, we will follow these steps:

### Step 1: Write the balanced chemical equation for the combustion of butane.
The balanced equation for the combustion of butane is:
\[ \text{C}_4\text{H}_{10} + \frac{13}{2} \text{O}_2 \rightarrow 4 \text{CO}_2 + 5 \text{H}_2\text{O} \]

### Step 2: Calculate the molar mass of butane (C4H10).
The molar mass of butane can be calculated as follows:
- Carbon (C): 12 g/mol × 4 = 48 g/mol
- Hydrogen (H): 1 g/mol × 10 = 10 g/mol
- Total molar mass of butane = 48 g/mol + 10 g/mol = 58 g/mol

### Step 3: Determine the amount of oxygen required for the combustion of butane.
From the balanced equation, we see that 1 mole of butane requires \(\frac{13}{2}\) moles of oxygen for complete combustion.

### Step 4: Calculate the molar mass of oxygen (O2).
The molar mass of oxygen (O2) is:
- Oxygen (O): 16 g/mol × 2 = 32 g/mol

### Step 5: Calculate the mass of oxygen required for the combustion of 58 g of butane.
Using the stoichiometry from the balanced equation:
- 1 mole of butane (58 g) requires \(\frac{13}{2}\) moles of oxygen.
- Mass of oxygen required = \(\frac{13}{2} \times 32\) g = 208 g

### Step 6: Calculate the amount of oxygen required for 1 kg of butane.
Since we have calculated the oxygen required for 58 g of butane, we can find the amount required for 1 kg (1000 g):
- Oxygen required for 1 kg of butane = \(\frac{208 \text{ g}}{58 \text{ g}} \times 1000 \text{ g}\)

Calculating this gives:
\[ \text{Oxygen required} = \frac{208}{58} \times 1000 \approx 3586.21 \text{ g} \]
Converting grams to kilograms:
\[ \text{Oxygen required} \approx 3.586 \text{ kg} \]

### Conclusion:
The amount of oxygen required for the combustion of 1 kg of the mixture of butane and isobutane is approximately **3.58 kg**.

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